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David G
06-06-2015, 11:14 PM
So here's the puzzle --

A bat and a ball cost \$1.10 between them. The bat costs \$1 more than the ball. How much does each cost?

How many of you got it wrong the first time?

TerryLL
06-06-2015, 11:31 PM
Seriously? Five cents and a dollar five cents.

Nicholas Carey
06-06-2015, 11:35 PM
Lessee...

x + (1+x) = 1.10

2x+1 = 1.10

2x = 0.10

X = 0.05

The ball cost 5 cents; the bat cost \$1.05

Jimmy W
06-06-2015, 11:47 PM
Seriously? Five cents and a dollar five cents.
Yep.

David G
06-07-2015, 12:20 AM
Ha! You will have to do better than that to trap this crowd, Mister G!:)

I'm finding the range. The last one I did... very few could solve. Oh... a couple did, but most mucked it up, and argued endlessly about it. My fault - as I posted without having a published authoritative solution ready to hand.

This one's pretty simple, granted. But I bet there were people who - at first glance - said Ten cents & One dollar. Now... getting them to admit it... that's another story <G>

seanz
06-07-2015, 01:16 AM
I'm finding the range. The last one I did... very few could solve. Oh... a couple did, but most mucked it up, and argued endlessly about it. My fault - as I posted without having a published authoritative solution ready to hand.

I asked The Smartest Person I Know, and she said it was a lazy question. And, you still don't have a published authoritative solution, do you? Hmm?

This one's pretty simple, granted. But I bet there were people who - at first glance - said Ten cents & One dollar. Now... getting them to admit it... that's another story <G>

Then there are other people that thought that was far too cheap for a bat and ball and weren't buying. Nuh-uh!

seanz
06-07-2015, 01:38 AM
:)

purri
06-07-2015, 03:21 AM
heh, heh...

John Smith
06-07-2015, 08:00 AM
Actually, it is a cute question and will likely be answered wrong by most who don't pause to do the thinking.

I remember some old questions of this nature;

A ship is floating in the harbor. A rope ladder hangs over the side. Rungs are 1' apart and 10 rungs are showing. Tide comes in 4'. How many rungs are showing?

Jim, to qualify for the midget car race has to do two one mile laps and average at least 60 mph. He has problems the first lap and only does 30 mph. How fast must he drive the second mile lap to bring his average speed to 60?

And one I wrote in junior high: A phonograph album is 12 inches in diameter to the outermost groove and 6 inches in diameter to the innermost groove. There are 100 grooves per inch of diameter. How far does the needle travel during the play of the record?

My oldest daughter had one class where she came home daily with this type of thing. I believe it helped her be good at thinking.

Jim Mahan
06-07-2015, 08:05 AM
Solving puzzles is perhaps the quintessential human trait; it leads to tool-building and other progress like the invention of stored memory as in writing and reading. Not only does regular exercise of your cerebral cortex help stave off advancing decrepitude, and amaze your friends, it also gets your head used to the function, so that when the sh)t h)ts the fan, you will be less likely to stand in one place, quivering, and repeating OMG, OMG, OMG, and more likely to resume breathing, put the fire out, pull the tyke from the path of the oncoming thing, get the boat back out of the ditch, or work toward meaningfully reducing economic disparity, pumping up voter turnout, or killing off MRSA. Sometimes you need to be able to think quickly, in terms of heartbeats, and sometimes you need to think deeply. One also needs to be aware that some things thought deeply about will have rewarding solutions that won't ever be apparent by using some conventional or rote answer, in the interstices between the boxes. The key thing for security and progress, is not just deep or rigorous thinking, but correct and appropriate answers. A general plenitude of practical successes, based on the scientific method, whether formally articulated as such or not, is required for survival and progress, the continuation of which will allow the fulfilling of our human potential, rather better than focusing on making a handful of rich sociopaths richer. Onward through the fog!

Celebrate the fringe, it's where the pioneers live. Now back to your regularly scheduled puzzlement.

Keith Wilson
06-07-2015, 08:15 AM
The instant fast-thinking answer is obviously \$1, which should set off alarms that that the obvious answer is wrong. You then have to slow down and think about it to get it right.

The spiral-groove problem requires some fancy math to get an accurate answer, although a close approximation is simple.

TerryLL
06-07-2015, 08:32 AM
Here's one for the math savants:

Two 40' poles stand over a perfectly flat field some distance apart. A rope is attached to the very top of each pole, spanning the distance between them.

The rope is not taught, but drapes down in the center and just touches the earth in one spot.

Assume that no external force, other than gravity, is responsible for the shape of the rope hanging between the poles.

If the length of rope between the two poles is exactly eighty feet, and touches the ground in the exact center between the poles, how far apart are the poles?

Keith Wilson
06-07-2015, 08:36 AM
Assuming the rope doesn't stretch due to its own weight? No distance apart at all - or, let's say 2X the diameter of the rope. :d

TerryLL
06-07-2015, 08:48 AM
Dang!

David G
06-07-2015, 09:16 AM
I asked The Smartest Person I Know, and she said it was a lazy question. And, you still don't have a published authoritative solution, do you? Hmm?

Then there are other people that thought that was far too cheap for a bat and ball and weren't buying. Nuh-uh!

Elitist snob. Limousine Liberal... likely <G>

Keith Wilson
06-07-2015, 11:32 AM
Dang!If it makes you feel any better. I was looking up the formulas for caternary arcs when I figured I'd better look at the numbers again. :D

TerryLL
06-07-2015, 11:53 AM
If it makes you feel any better. I was looking up the formulas for caternary arcs when I figured I'd better look at the numbers again. :D

Yep, that helps.

David G
06-07-2015, 12:18 PM
And I was trying to remember the term 'caternary'... so I could look up the formulas. Until I re-read it.

CWSmith
06-07-2015, 12:42 PM
And one I wrote in junior high: A phonograph album is 12 inches in diameter to the outermost groove and 6 inches in diameter to the innermost groove. There are 100 grooves per inch of diameter. How far does the needle travel during the play of the record?

Interesting lesson in test taking. There are multiple interpretations for "how far". Does it mean relative to the phonograph or the platter? Do you include the length of the arm and the arc? One assumes the 2nd because the extra information is given.

Just under 34,000 inches. Oops! You said diameter, not radius. Make that 8478 inches.

TerryLL
06-07-2015, 01:30 PM
And one I wrote in junior high: A phonograph album is 12 inches in diameter to the outermost groove and 6 inches in diameter to the innermost groove. There are 100 grooves per inch of diameter. How far does the needle travel during the play of the record?

Just a tad over 6 inches, depending on the length of the tone arm.

Tom Wilkinson
06-07-2015, 01:36 PM
Just a tad over 6 inches, depending on the length of the tone arm.

3", maybe slightly (miniscule amount) more if the tonearm travels in an arc but not all of them do.

David G
06-07-2015, 01:55 PM
I'm not sure where the 3" comes from. I'm thinking it's 6" + whatever tiny amount might be added by the angle of the arm.

A far more challenging (for me, anyway) calculation would be the question about the distance the needle travels in the groove thru all those revolutions of slowly decreasing circumference.

TerryLL
06-07-2015, 02:00 PM
3", maybe slightly (miniscule amount) more if the tonearm travels in an arc but not all of them do.

Yup, 3 inches. Too many rum toddies last night.

Tom Wilkinson
06-07-2015, 02:09 PM
I'm not sure where the 3" comes from. I'm thinking it's 6" + whatever tiny amount might be added by the angle of the arm.

A far more challenging (for me, anyway) calculation would be the question about the distance the needle travels in the groove thru all those revolutions of slowly decreasing circumference.

Only travels across one half of the disk.

CWSmith
06-07-2015, 02:17 PM
A far more challenging (for me, anyway) calculation would be the question about the distance the needle travels in the groove thru all those revolutions of slowly decreasing circumference.

See #19.

John Smith
06-07-2015, 05:19 PM
The instant fast-thinking answer is obviously \$1, which should set off alarms that that the obvious answer is wrong. You then have to slow down and think about it to get it right.

The spiral-groove problem requires some fancy math to get an accurate answer, although a close approximation is simple.

Actually, it's the record that spins. The needle simply goes across the radius; 3".

John Smith
06-07-2015, 05:22 PM
Yup, 3 inches. Too many rum toddies last night.

I was kind of proud of myself for thinking up that little puzzle.

John Smith
06-07-2015, 05:25 PM
See #19.

If I were to figure that out, I'd compute the circumference of the inner most groove and the outer most groove. Then I'd divide that by two to get the average, which I would then multiply by 300. Not 100% sure that works accurately, but it would seem to.

Keith Wilson
06-07-2015, 05:26 PM
The needle simply goes across the radius; 3".Erk. I could quibble about arcs and stuff, or travel relative to what (if you wanted to figure needle wear, for example, the length of the groove would be important), but the truth is I just missed the obvious. :d Not the first time.

That 'average circumference' method was what I was talking about to get a close answer, but not perfect. The exact true length of the spiral is harder.

CWSmith
06-07-2015, 05:55 PM
If I were to figure that out, I'd compute the circumference of the inner most groove and the outer most groove. Then I'd divide that by two to get the average, which I would then multiply by 300. Not 100% sure that works accurately, but it would seem to.

Interesting. I just did the integration...

I can guarantee you that the needle passes through far more than 3 inches of groove platter.

CWSmith
06-07-2015, 05:56 PM
...but the truth is I just missed the obvious.

No, the question was ill-posed and ambiguous.

Tom Wilkinson
06-07-2015, 06:33 PM
No, the question was ill-posed and ambiguous.

No it wasn't. The needle moves three inches. The disc moves below it. The question never asked what the length of groove tracked was. Grab the tone arm and move it. What is the maximum distance it can move. The needle distance has to be less than that.

David G
06-07-2015, 06:36 PM
Only travels across one half of the disk.

Gort it.

CWSmith
06-07-2015, 07:58 PM
No it wasn't. The needle moves three inches. The disc moves below it. The question never asked what the length of groove tracked was. Grab the tone arm and move it. What is the maximum distance it can move. The needle distance has to be less than that.

First, the question was how far does the needle move, not the tone arm. As Keith points out, it's the distance in the groove that is of greatest interest.

Second, if the answer is 3 inches, don't you think the questions is stupefyingly simple? All you need to know is the definition of radius.

There is ambiguity in the question and multiple answers.

Tom Wilkinson
06-07-2015, 08:03 PM
The needle can't move further than the tone arm. It's attached to it. All the other info was thrown in as a distraction, and it worked.
One revolution of the disc doen't not move the needle more than a few thousands, not 37+ inches.

CWSmith
06-07-2015, 08:36 PM
The needle can't move further than the tone arm. It's attached to it. All the other info was thrown in as a distraction, and it worked.
One revolution of the disc doen't not move the needle more than a few thousands, not 37+ inches.

OK, Tom. It's not worth the argument.

Keith Wilson
06-08-2015, 07:19 AM
No, the question was ill-posed and ambiguous.No, it was specifically designed to be tricky. There's a whole class of trick questions that appear to be complicated, and actually are if you just dive right into the math without thinking about it much, but reduce to something trivial if you think about it. I thing the idea is to get you to slow down and not go with your initial impulse for a route to a solution. The one about the rope and the length of the caternary curve is another example of the type.

CWSmith
06-08-2015, 08:41 AM
No, it was specifically designed to be tricky. There's a whole class of trick questions that appear to be complicated, and actually are if you just dive right into the math without thinking about it much, but reduce to something trivial if you think about it. I thing the idea is to get you to slow down and not go with your initial impulse for a route to a solution. The one about the rope and the length of the caternary curve is another example of the type.

No, Keith, if you read #19 you will see that I considered both interpretations and another and chose what I still think is correct.

Let me put it this way: If you tell a friend you have a "brain teaser" and give them this with the answer 3 inches, he'll try to sell you a bridge.

Tom Wilkinson
06-08-2015, 11:28 AM
Spin it whatever way you like, the needle, being physically attached to the tonearm cannot possible travel any further than what the tonearm can move. The question was designed to decieve.

You have an odd definition of of the word move in this context.

TerryLL
06-08-2015, 11:43 AM
How far does the needle travel during the play of the record?

That was the question posed.

Not, how much record groove passed under the needle.

Let's move on.

CWSmith
06-08-2015, 11:46 AM
Spin it whatever way you like, the needle, being physically attached to the tonearm cannot possible travel any further than what the tonearm can move. The question was designed to decieve.

You have an odd definition of of the word move in this context.

Actually, the definition of motion is relative.

Jump on a tread mill, run a mile, then say you didn't move.

John Smith
06-08-2015, 11:50 AM
Actually, the definition of motion is relative.

Jump on a tread mill, run a mile, then say you didn't move.

That's true. The treadmill did the moving. In my question, the NEEDLE does move; across the radius of the grooves.

Tom Wilkinson
06-08-2015, 11:53 AM
Actually, the definition of motion is relative.

Jump on a tread mill, run a mile, then say you didn't move.

Um, that's the whole point of the treadmill, to exersize without actually moving. Sure you ran your legs like crazy and your heart rate went up, but you didn't go anywhere.

Kind of like a stationary bicycle.

Either way, the needle isn't moving much. In relation to anything in the entire room and the rest of the earth, the needle moves 3". Lots of groove travels past the needle, but that's a whole different question.

Keith Wilson
06-08-2015, 12:01 PM
It depends on what you're trying to calculate. You might want to know how far the needle moves along the groove in order to calculate how much music you can fit on a given size record, or how fast the needle wears. And of course all motion is relative to a reference frame - but the standard reference frame is normally the planet we're sitting on, not a spinning disk, unless the problem definition specifically says otherwise.

CWSmith
06-08-2015, 12:04 PM
It depends on what you're trying to calculate. You might want to know how far the needle moves along the groove in order to calculate how much music you can fit on a given size record, or how fast the needle wears. And of course all motion is relative to a reference frame - but the standard reference frame is normally the planet we're sitting on, not a spinning disk, unless the problem definition specifically says otherwise.

In that case, are we all in agreement that what constitutes a "brain tease" in The Bilge is the question, "What is half of 12 minus 6?"?

Captain Intrepid
06-08-2015, 12:05 PM
If we get to make arbitrary selections of reference frames, the needle doesn't move at all, the record player simply swings below it.

;)

John of Phoenix
06-08-2015, 12:07 PM
I was kind of proud of myself for thinking up that little puzzle.That would have been a good one for the Puzzler on "Car Talk". Just enough obfuscation. Clearly.

Harvey Golden
06-08-2015, 01:10 PM
I came up with 346.6miles and 3 inches for how far the needle moved. What did I do wrong? Was I not supposed to factor in the speed of the Earth's rotation for ~20 minutes?

BrianY
06-08-2015, 01:22 PM
How many grooves are there on the record?

Tom Wilkinson
06-08-2015, 01:38 PM
How many grooves are there on the record?

1.0

Keith Wilson
06-08-2015, 01:43 PM
The needle moves about 1177'-6" along the groove. The needle moves a touch over 3" relative to the base of the turntable.

Tom Wilkinson
06-08-2015, 01:47 PM
Why 6"? It only is going to move across half of the grooved portion of the record.

Rum_Pirate
06-08-2015, 02:10 PM
http://forum.woodenboat.com/images/misc/quote_icon.pngOriginally Posted by BrianYhttp://forum.woodenboat.com/images/buttons/viewpost-right.png
(http://forum.woodenboat.com/showthread.php?p=4563233#post4563233)How many grooves are there on the record?
1.0

Two. One on each side. |;)

Tom Wilkinson
06-08-2015, 02:18 PM
Two. One on each side. |;)

true, but not always. some records only are grooved on one side, some have more than one groove per side

Keith Wilson
06-08-2015, 02:29 PM
Why 6"?Duh. Moving too fast, sorry. 3", of course.

John Smith
06-08-2015, 05:17 PM
That would have been a good one for the Puzzler on "Car Talk". Just enough obfuscation. Clearly.

Today there are some who would ask, "What's a record?" or "What's a needle?" A chance to ponder how things change.